252edt
| ← 251edt | 252edt | 253edt → |
252 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 252edt or 252ed3), is a nonoctave tuning system that divides the interval of 3/1 into 252 equal parts of about 7.55 ¢ each. Each step represents a frequency ratio of 31/252, or the 252nd root of 3.
252edt is nearly identical to 159edo, but with the perfect twelfth instead of the octave tuned just. Like 159edo, 252edt is consistent to the 18-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.04 | +0.00 | +0.09 | -1.31 | +0.04 | -2.67 | +0.13 | +0.00 | -1.27 | -0.23 | +0.09 |
| Relative (%) | +0.6 | +0.0 | +1.1 | -17.3 | +0.6 | -35.3 | +1.7 | +0.0 | -16.8 | -3.0 | +1.1 | |
| Steps (reduced) |
159 (159) |
252 (0) |
318 (66) |
369 (117) |
411 (159) |
446 (194) |
477 (225) |
504 (0) |
528 (24) |
550 (46) |
570 (66) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -2.62 | -1.31 | +0.17 | +0.88 | +0.04 | -2.99 | -1.22 | -2.67 | -0.18 | -1.66 | +0.13 |
| Relative (%) | -34.9 | -34.8 | -17.3 | +2.3 | +11.7 | +0.6 | -39.6 | -16.2 | -35.3 | -2.4 | -22.1 | +1.7 | |
| Steps (reduced) |
588 (84) |
605 (101) |
621 (117) |
636 (132) |
650 (146) |
663 (159) |
675 (171) |
687 (183) |
698 (194) |
709 (205) |
719 (215) |
729 (225) | |
Subsets and supersets
Since 252 factors into primes as 22 × 32 × 7, 252edt has subset edts 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, and 126.